It is often desirable to evaluate capabilities and electrical characteristics of electrical equipment, such as transmitters. Such an evaluation can provide an indication of the operating condition of the equipment. When the equipment being tested is a transmitter, an evaluation of the transmitter's electrical characteristics typically involves correlation of a reference signal with data and a signal that is being transmitted by the transmitter.
An example of such a correlation is cross-correlation. As is known, cross-correlation is a standard method of estimating the degree to which two series of data are correlated. For two series x(i) and y(i), where i=0, 1, 2, . . . n−1 and mx and my are means of the correspondence series, the cross-correlation r is given by the formula:
                    r        =                                            ∑              i                        ⁢                          [                                                (                                                            x                      ⁡                                              (                        i                        )                                                              -                    mx                                    )                                *                                  (                                                            y                      ⁡                                              (                                                  i                          -                          d                                                )                                                              -                    my                                    )                                            ]                                                                                            ∑                  i                                ⁢                                                      (                                                                  x                        ⁡                                                  (                          i                          )                                                                    -                      mx                                        )                                    2                                                      ⁢                                                            ∑                  i                                ⁢                                                      (                                                                  y                        ⁡                                                  (                                                      i                            -                            d                                                    )                                                                    -                      my                                        )                                    2                                                                                        (        1        )            
In equation (1), the term “d” represent the group delay between the comparing signals. For this application, the latency between the reference signal and the received data streams is d=0. FIG. 1 shows an exemplary graph 10 of correlation of two series of data. A first series of data is a pulse 12, and a second series of data is a pulse 14. Correlation of the pulses 12 and 14 is shown in a correlation series 16. It will be appreciated that the pulse 14 is being “slid” past the pulse 12. At each shift, the sum of the product of the newly lined-up terms in the series is solved. The sum is large when the delay shift is such that similar structures line up or coincide. In the exemplary graph 10, maximum correlation is achieved for a delay of 3—that is, when the pulses 12 and 14 line up or coincide with each other. As is also known, maximum correlation is normalized to a value +1 and an anti-correlation normalizes to a value of −1.
Current methods of determining electrical characteristics using cross-correlation techniques employ manual derivation of electrical characteristics. Another current method entails extensive post-processing of the transmitted signal.
In the current methods, once the delays are encountered, therefore, any transmitter problems will not be known while the transmitter is in use. As such, the transmitter can be used with faults that are unknown, because the transmitter cannot be tested until after a lengthy delay.
It would therefore be desirable to evaluate a transmitter's capabilities and electrical characteristics in real-time. However, there is an unmet need in the art for evaluating a transmitter's capabilities and electrical characteristics in real time.